Purpose: The reason for perceptual alternations during binocular rivalry remains debatable. Some believe that neural adaptation plays a key role in the alternation process while others construe alternations as an adaptive sampling of possible perceptual interpretations driven by an intrinsic oscillator. Using a novel display procedure, we have found that rivalry alternations can be substantially slowed when the rival targets themselves continuously move around the visual field, constantly shifting their neural representations onto fresh, unadapted neural tissue. Methods: During 2-min observation periods, observers maintained strict central fixation and used keypresses to report binocular rivalry alternations. On some trials the rival targets moved smoothly in tandem around an imaginary circle centered on the fixation point, and on the remaining trials the targets remained stationary at a given location on the circle's circumference. Results: Among a large sample of observers, dominance durations during the “moving” condition were typically quite long compared to their “stationary” durations, resulting in significantly slower alternation rates when the rival targets moved. Alternation rates were not slowed, however, when observers used pursuit eye movements to track the moving targets, thereby keeping the images of the targets on approximately the same retinal location. Alternations were reliably triggered when rival targets passed through a local region of the visual field that had been preadapted to one of the rival targets. There was no tendency for alternations, when they did occur, to coincide with transitions from one hemisphere to the other. Conclusions: Continuous movement of the rival targets may preclude local neural adaptation, leading to a relatively stable balance between excitatory and inhibitory interactions between the two competing neural representations.